Empirical bounds on \(Z^{\prime }\)  couplings exist for these kinds of models. Such bounds depend on the mass scale of \(Z^{\prime }\) . High energy colliders are sensitive to \(M_{Z^{\prime }}\gtrsim 10\)  GeV and the constraints for lighter \(Z^{\prime }\) 's are given mainly by precision QED observables, \(B\)  meson decay and some fixed target experiments [1]}.
Besides these constraints, there is also a constraint on the lifetime of a \(Z^{\prime }\) . Its lifetime should be less than one second in order to guarantee that the \(Z^{\prime }\)  decays before the onset of big-bang nucleosynthesis [2]}. As a consequence, the secluded DM fermion will annihilate preferably into a \(Z^{\prime }\)  pair [3]}.
